4.4. Systematic uncertainties in the determination of _m

The above values differ sensitively from several recent analyses on the same test and using the same high redshift sample. It is therefore important to identify the possible source of systematic uncertainty that may explain these differences. The test is based on the evolution of the mass function (Blanchard and Bartlett, 1998). The mass function has to be related to the primordial fluctuations. The Press and Schechter formalism is generally used for this, and this is what used in deriving the above numbers. However, this may be slightly uncertain. Using the more recent form proposed by Governato et al. (1999) we found a value for _m slightly higher (a different mass function was used in Figure 1). A second problem lies in the mass temperature relation which is necessary to go from the mass function to the temperature distribution function. The mass can be estimated either from the hydrostatic equation or from numerical simulations. In general hydrostatic equation leads to mass smaller than those found in numerical simulations (Roussel et al., 2000; Markevitch, 1998; Reiprich and Böhringer, 2002; Seljak, 2002). Using the two most extreme mass-temperature relations inferred from numerical simulations, we found a 10% difference. We concluded that such uncertainties are not critical.

Another serious issue is the local sample used: using HA sample we found a value smaller by 40%. Identically, if we postulated that the high redshift abundance has been underestimated by a factor of two, _m is reduced by 40%. The determination of the selection function of EMSS is therefore critical. An evolution in the morphology of clusters with redshift would result in a dramatic change in the inferred abundance (Adami et al., 2001). This is the most serious possible uncertainty in this analysis. However, the growing evidences for the scaling of observed properties of distant clusters (Neumann and Arnaud, 2001), rather disfavor such possibility.